Nonlinear anisotropic deformation behavior of a graphene monolayer under uniaxial tension

Based on first principle calculations, a graphene monolayer shows a complicated deformation behavior under uniaxial tension. The maximum stress of graphene is reached when the bond stretching ratio is far less than its breaking value, which means that graphene shows the typical "ductile-like" behavior but not the conventionally considered "brittle-like" behavior. Although the graphene monolayer shows isotropic behavior in strength, it is strongly anisotropic in deformation (i.e., the ultimate strain is highly different along the different directions). Under uniaxial tension along the zigzag/armchair direction, the overall deformation is only supported by the C-C bonds in one orientation, whereas the C-C bonds in the other orientation and the C-C-C bond angle have almost no contribution, which cannot be correctly predicted by the empirical potential simulations. The complicated bond deformation means that the conventional constitutive model (σ = Eε + Dε(2)) cannot accurately describe the tensile behavior of the graphene monolayer. According to the bond deformation under uniaxial tension, graphene can be simplified as a spring-network including both nonlinear springs (resisting both the tensile and compressive load) and a very strong compressive angle-spring (resisting the decrease of the C-C-C bond angle).